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Three-Dimensional Shape Modeling and Analysis of Brain Structures
05:33

Three-Dimensional Shape Modeling and Analysis of Brain Structures

Published on: November 14, 2019

A Computational Model of Multidimensional Shape.

Xiuwen Liu1, Yonggang Shi, Ivo Dinov

  • 1Department of Computer Science, Florida State University, Tallahassee, FL 32306, USA.

International Journal of Computer Vision
|November 9, 2010
PubMed
Summary
This summary is machine-generated.

This study introduces a computational shape model for complex, multidimensional objects using elastic deformations. It enables quantitative analysis of shape variations and dynamics, crucial for fields like brain mapping.

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Area of Science:

  • Computational geometry
  • Differential geometry
  • Medical image analysis

Background:

  • Existing Riemannian models primarily focus on curves.
  • Multidimensional objects require advanced shape representation.
  • Quantifying shape variation is essential for comparative studies.

Purpose of the Study:

  • To develop a computational model for multidimensional shapes of general topological types.
  • To establish geodesic metrics for measuring shape interpolation costs via elastic deformations.
  • To create a unified framework for statistical shape modeling, comparison, and dynamics.

Main Methods:

  • Utilizing a discrete exterior derivative of parametrizations over a finite simplicial complex for shape representation.
  • Constructing Riemannian shape spaces with geodesic metrics.
  • Developing algorithms for geodesic calculations and local/global shape similarity quantification.

Main Results:

  • A novel computational model extending Riemannian geometry to general multidimensional shapes.
  • Algorithms for computing geodesics and distances, enabling quantitative shape analysis.
  • A framework integrating local and global shape dissimilarities, accounting for regional variations.

Conclusions:

  • The developed Riemannian shape spaces offer a versatile framework for diverse shape analysis problems.
  • The model facilitates statistical modeling, inter-individual shape comparison, and dynamic shape simulation.
  • Applications demonstrated in brain mapping highlight its utility in analyzing anatomical variation from neuroimaging data.